Functional Data Analysis Based On Generalized Gaussian Process Regression

With the increasingly rapid development of the computer, the ability to obtain data also improved, data samples thus rendered even more complex, which requires that we can not use tra-ditional methods of data analysis.So, a new method called functional data analysis appeared. In this paper,we combine functional data analysis with Gaussian process regression models,describe basic characteristics of functional data,and introduce the step of Gaussian process regression modeling and parameter estimation as well as forecasting process. Then on the base,we propose the gener-alized Gaussian process concurrent regression model for functional data on which the functional response variable has a binomial, Poisson or other non-Gaussian distribution from an exponential family,while the covariate are mixed functional and scalar variables.This proposed model others a nonparametric generalized concurrent regression method for functional data with multi-dimensional covariates, providing a natural framework on modeling common mean structure and covariance structure simultaneously for repeatedly observed functional data. The mean structure can be used to catch up the overall information about the observations, while the covariance structure provides the characteristic of each individual batch. The definition of the model, the implementation and the inference as well as its asymptotic properties are discussed.